Two-dimensional charged-exciton complexes

A simple method is used to calculate the binding energies of negatively and positively charged excitons (trions) in an ideal two-dimensional electron-hole system. The binding energy of the charged exciton is obtained as a function of the mass ratio σ=${\mathrm{m}}_{\mathrm{e}}$/${\mathrm{m}}_{\mathrm{h}}$, using a mass-weighted coordinate system, thus avoiding tedious variational calculations. Our calculated values of the binding energies of charged excitons agree well with existing experimental and theoretical results. The calculations are extended to determine the binding energy of the two-dimensional charged-biexciton complex.